Ruin probability for an insurer investing in several risky assets
Author:
M. V. Bratyk
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 77 (2008), 1-13
MSC (2000):
Primary 60G44, 60H30; Secondary 62P05, 60K10
DOI:
https://doi.org/10.1090/S0094-9000-08-00743-6
Published electronically:
January 14, 2009
MathSciNet review:
2432768
Full-text PDF Free Access
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Additional Information
Abstract: The ruin probability of an insurer is studied for the classical Cramér–Lundberg model with finite exponential moments. The nonclassical property of the model considered in the paper is the possibility to invest in two different risky assets (which may be dependent) whose price processes are either described by geometric Brownian motions or are semimartingales with absolutely continuous characteristics with respect to Lebesgue measure. We study the ruin probability for the case where a free credit is not available in the money market and where the insurer can invest in a finite number of risky assets whose price processes are described by jointly independent Brownian motions.
References
- J. Gaier, P. Grandits, and W. Schachermayer, Asymptotic ruin probabilities and optimal investment, Ann. Appl. Probab. 13 (2003), no. 3, 1054–1076. MR 1994044, DOI https://doi.org/10.1214/aoap/1060202834
- Yulīya Mīshura, An estimate for the ruin probability for models with long-term dependence, Teor. Ĭmovīr. Mat. Stat. 72 (2005), 93–100 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 72 (2006), 103–111. MR 2168140, DOI https://doi.org/10.1090/S0094-9000-06-00668-5
- Alexander Melnikov, Risk analysis in finance and insurance, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, vol. 131, Chapman & Hall/CRC, Boca Raton, FL, 2004. Translated from the Russian manuscript and edited by Alexei Filinkov. MR 2013235
- A. V. Mel’nikov, Risk Management. Stochastic Analysis of Risks in Finance and Insurance, “Ankil”, Moscow, 2001. (Russian)
- A. V. Boĭkov, The Cramer-Lundberg model with stochastic premiums, Teor. Veroyatnost. i Primenen. 47 (2002), no. 3, 549–553 (Russian, with Russian summary); English transl., Theory Probab. Appl. 47 (2003), no. 3, 489–493. MR 1975908, DOI https://doi.org/10.1137/S0040585X9797987
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References
- J. Gaier, P. Grandits, and W. Schachermayer, Asymptotic ruin probabilities and optimal investment, Ann. Appl. Probab. 13 (2003), no. 3, 1054–1076. MR 1994044 (2004k:91124)
- Yu. S. Mishura, An estimate for the ruin probability for models with long-term dependence, Teor. Imovir. Mat. Stat. 72 (2005), 93–100; English transl. in Theory Probab. Math. Statist. 72 (2006), 103–111. MR 2168140 (2007b:60164)
- A. V. Mel’nikov, Risk Analysis in Finance and Insurance, Chapman and Hall/CRC, 2004. MR 2013235 (2004i:91004)
- A. V. Mel’nikov, Risk Management. Stochastic Analysis of Risks in Finance and Insurance, “Ankil”, Moscow, 2001. (Russian)
- A. V. Boikov, The Cramér–Lundberg model with stochastic premiums, Teor. Veroyatnost. i Primenen. 47 (2002), no. 3, 549–553; English transl. in Theory Probab. Appl. 47 (2003), no. 3, 489–493. MR 1975908 (2004d:60228)
- N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland Publishing Co. and Kodansha, Ltd., Amsterdam–New York and Tokyo, 1981. MR 637061 (84b:60080)
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Additional Information
M. V. Bratyk
Affiliation:
Department of Mathematics, Faculty for Informatics, National Kyiv Mohyla University, Skovoroda Street, 2, Kyiv, 04070, Ukraine
Email:
mbratyk@ukr.net
Keywords:
Cramér–Lundberg model,
ruin probability,
investment strategy,
geometric Brownian motion
Received by editor(s):
July 17, 2006
Published electronically:
January 14, 2009
Article copyright:
© Copyright 2008
American Mathematical Society
